To even begin a coherent discussion of Yeat's poem, one should first read his book A Vision, along with an historical understanding of his involvement with the Theosophical Society. Graham Hough, one of Yeats' biographer's states "...Graham Hough is of the opinion that �again and again we find that obscure, puzzling and apparently original elements in Yeats�s esoteric doctrine, even towards the end of his life, turn out to have their roots in the Theosophical teaching he first encountered in his early twenties�..."
This exposure and the Sitz in Leben (1920's) of this work certainly examines his spiritual reflections, in my opinion. Your particular phrase is difficult to isolate for analysis, but, as with much of the rest of the short work, has overtly religious conotations. The "blood-dimmed" quality has a dual source... the impact of all that occurred in the recent Great War as well as Yeats' belief that religious structures, especially Christian vs Pagan went through cyclical changes ("gyres") that were difficult to grasp.
The Irish Rebellion and subsequent bloodshed also plays a part in the construction of the poem. Although not an ardent Republican, Yeats' infatuation with Maud Gonne influenced his work for most of his life, (see especially, Easter 1916)and I believe, is reflected in the piece as well.
At any rate, the line in question has as its basis the sometimes bloody scenes found in The New Testament Book of The Revelation of St John the Divine and their connections to the passing away of old orders and the arrival of the new... Other's will disagree, but that's the true value of Yeats, again, in my opinion...